Now, brothers and sisters, I have applied these things to myself and Apollos for your benefit, so that you may learn from us the meaning of the saying, “Do not go beyond what is written.” Then you will not be puffed up in being a follower of one of us over against the other.

What does the "saying" he refers to mean? Was it a local saying? Something Paul is just introducing now? And what does is the referent of "what is written?" Is it the Scriptures? Paul's own writing here in 1 Corinthians? Something else?

3 Answers
3

There probably is no "saying"

The whole phrase "meaning of the saying" is not in the Greek manuscripts (at least not in Nestle-Aland nor Byzantine Majority), and thus is added by the NIV translators. No other major translations add those words, and they appear to confuse the issue in doing so (however, the discussion below will point to why they probably did).1

Verse Analysis

There is a slight variation of significance here between the two text types. The passage reads in the majority text (extra comments and significant variations with the Nestle-Aland text noted by bracket numbers):

Ταῦτα δέ ἀδελφοί μετεσχημάτισα[1] εἰς ἐμαυτὸν καὶ Ἀπολλὼ[2] διʼ ὑμᾶς
These things then, brethren, I have transformed to myself and Apollos, for the sake of you,
ἵνα ἐν ἡμῖν μάθητε τὸ [3] μὴ ὑπὲρ ὃ[4] γέγραπται[5] φρονεῖν[6]
in order that in us you may learn the not above what is written to think
ἵνα μὴ εἷς ὑπὲρ τοῦ ἑνὸς φυσιοῦσθε κατὰ τοῦ ἑτέρου.
in order that not one above the one may be puffed up against the other

[1] μετεσχημάτισα (meteschematisa): This word here "is unique,"2 meaning it is a figurative use of the term that is unique to that use in Scripture, and rare in other literature. The word literally means "to change" or "transform," including "to feign to be what one is not."3 Hence the various translations of "in a figure transferred" (KJV), "figuratively transferred" (NKJV), "figuratively applied" (NASB), or simply "applied" (NIV/ESV).

[2] N-A spelling variation Ἀπολλῶν. Spelling variations in names are common in Biblical texts, but only sometimes significant (i.e. when the change may really point to another person).

[3] Here is where the missing phrase that was added by NIV would roughly be if it existed. More discussion about this point in [6].

[4] The ὃ (ho; "what") is a singular relative pronoun; N-A has a plural ἃ (ha; "what things"). Grammatically, the majority text is correct, because the word is the subject of the verb γέγραπται (gegraptai; "has been written") which is singular in form, and in Greek the number of the subject matches that of the verb (normally; there are exceptions for collective words). Here it is unlikely the variation changes meaning, because the singular would be looking at what was written as a whole, the plural at individual aspects of what was written within the whole.

[5] γέγραπται (gegraptai) is a perfect passive participle. Normally perfect passives are translated with the helper verbs in English of "has/have been," and thus "has been written." However, with this particular verb, it is common (and perfectly correct) to translate it as "is written." This is because the perfect tense carries the idea of a resulting state due to the action what was in the past performed, and in the case of something being written, then it remains written (unless of course all copies of it are destroyed). In a way, this word itself hints at the continued preservation of the text (though in and of itself, that would be pushing the meaning too far). What is important to note with this word is that "In the sphere of revelation, the written records hold this authoritative position, and gégraptai always implies an appeal to the indisputable and legal authority of the passage quoted [me: or in this case, referred to]."4 Normally it is applied to OT quotations in the introductory formula "it is written" with the OT quote following.

[6] This is the most significant variation, as the word φρονεῖν (fronein; "to have an opinion," or "to consider," or "to think")5 is missing in the N-A text. So it would read from N-A translated "you may learn the not above what is written," (i.e. "you may learn not beyond what is written"). This variation is what compelled the NIV translators (who are generally following N-A text) to attempt the resolution they did, as the τὸ ("the") is by itself, implying what follows is a "definite" something being referred to. So they are basing their translation "meaning of the saying" off of the presence of the definite article here that is making the following phrase definite. Thus the article is acting as a "substantiver" of the clause to make it into a direct object for the verb μάθητε (mathete; "you may learn").6 The construction is used before a "statement, quotation, or clause."7 It may be the NIV translators felt this should be treated as a quotation,8 and hence their translation. Another oddity in this variant is that the μη ("not") is used with non-indicative verbs, but γέγραπται (the only verb in association with it in the N-A text) is in the indicative mood. This leaves the verb that the μη is supposed to be modifying as elliptical (i.e. not present and needing to be supplied).9 In that translation the verbal idea of "go" is supplied by the translators.

In the majority text reading that has the trailing φρονεῖν, it is still functioning as a "substantiver" of the clause, but the clause is an infinitive phrase with this as a modifying clause because the φρονεῖν is in the infinitive form, and the neuter τὸ is regularly used in conjunction with the infinitive, especially when the infinitive is the direct object of a verb as here.10 The intervening μὴ ὑπὲρ ὃ γέγραπται joins that clause into the whole infinitive phrase (that is, the leading τὸ and the trailing infinitive φρονεῖν define the whole direct object). So they are not simply to "learn to think" but to "learn to not think above what is written." Note that this variant supplies the verb that μή was oddly missing in the other variant, as μή would be used with the infinitive form of verbs.

Conclusion: My particular bias for the majority text aside (disclaimer), simply working through the meaning of what it is saying leads me to favor the majority text reading as correct, as the phrase makes more sense to me in context with that reading. But I leave each of you to decide that for yourself.

Context Analysis

The fact that γέγραπται always refers to authoritative Scripture otherwise leads to a strong conclusion that such is intended here. For this reason, some believe it cannot refer to the preceding part of the letter.11

I personally do not have (1) a bias to exclude the possibility that Paul is simply using the term γέγραπται in a non-technical sense here, or (2) could in fact still be using it as a technical term, but relating such authority to what he had just written (especially in light of his statement in 4:1-5, but v.1 particularly, where he is making a statement of his authority).

That being so (i.e. not having the bias to reject it referring to previous context or that context being regarded as scripture), I believe the first part of v.6 in reference to the figurative transfer he has made using himself and Apollos (which refers back to 1 Cor 3:1-4:5) is clearly in view for the point of vv.6-7 here. That is, do not think of any other believer (yourselves included Paul is saying) above what any believer is,

part of "the temple of God" in whom "the Spirit of God dwells" (3:16), that must be kept holy (3:17)

not to be self deceived and a fool, but wise (3:18-20)

not proud, for there is an equality among believers, and all are under God (3:21-22)

respecting those serving Christ and being stewards of His word faithfully (4:1-5)

Such were Paul and Apollos, and so Paul has transformed himself and Apollos into this illustration of what each believer ought to be and what each ought to think of other believers.

Conclusion

For me, the answer of "what is written" is Paul's revelation he just made to Corinth about man's role in God's work.

Notes

1 This is a case, in my view, of why the NIV is not one of the better translations. Just a little too dynamic equivalent (i.e. interpretive) in its attempts to translate, and things like this creep in that to me just confuse the issues more. NOTE: don't read into that more than it says. I am not wholly against a certain level of dynamic equivalence in a good translation, I just think NIV goes too far, and the more literal translations keep that balanced.

2 William Arndt, Frederick W. Danker, and Walter Bauer. A Greek-English Lexicon of the New Testament and Other Early Christian Literature (Chicago: University of Chicago Press, 2000), s.v. μετασχηματίζω, 3. Hereafter referred to as BDAG.

8 BDAG, s.v. γράφω, 2.b, refers to 1 Cor 4:6 (the N-A form) as "a traditional formulation," but without any reference evidence prior to the composition of Corinthians, so the "traditional formulation," if such does exist, may be based off this version of this Scripture. Other lexicons note this as an idiom, but none give any proof (as I would have expected BDAG to).

9 I found this oddity noted of the N-A reading in both John Peter Lange, Philip Schaff, Christian Friedrich Kling, and Daniel W. Poor, A Commentary on the Holy Scriptures: 1 Corinthians (Bellingham, WA: Logos Bible Software, 2008), 93; and A.T. Robertson, Word Pictures in the New Testament (Nashville, TN: Broadman Press, 1933), 1 Corinthians 4:6. As to μή being used with the non-indicative mood, see BDAG, s.v. μή.

10 Wallace, 602 n.40.

11 Lange, 93. This commentary believes if the previous part of the letter was meant that

it would have been προέγραψα, I have before written (comp. Eph.
3:3). According to Paul’s usage, the formula: “it is written,” refers
to the Holy Scriptures, especially to the Old Testament: since we find
no allusion to any New Testament, or to any life of Christ in any of
Paul’s writings, ... Undoubtedly Paul here has in mind, not individual
expressions of Holy Writ, but its collective tenor, which all points
to this truth: that all honor belongs to God; and that all
self-boasting, all cleaving to men, and priding oneself in men, must
be given up. This doctrine we find summed up in apophthegms like Jer.
9:23, to which reference has already been made. (93)

wise master builders, with the Corinthians being a building under construction on the foundation of Jesus Christ (3:9b-12)

faithful stewards of God's mysteries (4:1-2)

spectacles to angels and to men (4:9)

fools for Christ's sake (4:10)

fathers (4:14-15)

These metaphors were apt descriptions of Paul's and Apollos's mission among the Corinthians. Clearly, the Corinthians wanted to go "beyond" these homey metaphors in favor of some nobler metaphors, titles, and labels for their favorite teachers (whether Paul, Apollos, Cephas, or Christ--1:12-13), labels such as

wise philosophers

powerful rhetors (public speakers) and persuaders

noble, strong leaders, not mere servants

men on a pedestal, as befitting heroes of the faith

Paul warns them, however, to stick with the metaphors he used in the letter he is writing to them, so as to avoid being puffed up with pride as a result of siding with their favorite apostle and banding together in a clique or coterie of likeminded believers. This partisan spirit was inconsistent with the humility demonstrated by Jesus and by the apostles themselves, including Paul, in the face of real hardships (see 4:11-13).

There are several views by the expositors for the meaning if this verse but I will only post the one that seems the most congruent to the immediate context. It would seem the simplest view is this: Paul is hoping that they might learn by the example of Paul and Apollos not to think to highly of men according to the general view of scripture that portrays ministers as mere servants who bring his bare word. To think 'highly of men' is obviously to go 'beyond' what is written in the Hebrew scriptures about the subject.

One sample expositor who was an expert in original languages takes this view:

And these things, brethren, I have in a figure transferred to myself and (to) Apollos for your sakes; that ye might learn in us not to think (of men) above that which is written, that no one of you be puffed up for one against another.
These things refers to what was said in the preceding chapter of preachers, especially to what is said from 3:5, and onwards. These things he had in a figure transferred to himself and Apollos. That is, instead of teaching in an abstract, general form, that ministers were mere servants, he had presented the truth in a concrete form, saying that he and Apollos were servants, mere instruments in the hand of God. This was the (μετασχηματισμός), the change of form which he had adopted. He did this, he says, that they might learn in we, i. e. by what I have said of Apollos and myself, not to think above that which is written. That is, not to estimate ministers above the scriptural standard. As Paul had been treating of this subject, above that which is written, might seem naturally to refer to what he himself had just written. But as the phrase always elsewhere refers to the Old Testament, which were the writings recognized as of divine authority, such is probably the reference here. He does not appeal to any one passage, but to the doctrine taught in the Scriptures concerning ministers of religion. The Corinthians were not to think of their ministers more highly than the Bible authorized them to think. Comp. Jer. 9:23, 24. The particle (ἵνα), rendered that, has its ordinary force, in order that, although the following verb (φυσιοῦσθε,) is in the indicative, a combination which occurs nowhere else except in Gal. 4:17. The connection is with the preceding clause, ‘That ye may learn to think correctly, in order that,’ &c. (AN EXPOSITION
of the FIRST EPISTLE TO THE CORINTHIANS by CHARLES HODGE, D. D., p70)